Theory of Nonlinear Waves.
INNSBRUCK UNIV (AUSTRIA) INST FOR THEORETICAL PHYSICS
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The paper is a review of papers which handle nonlinear waves with an averaging technic developed by Whitham. If it is possible to derive the differential equations governing the problem from a variational principle the Lagrangian can be averaged over one period. From the averaged Lagrangian averaged conservation equations are derived and from these one finds a second order differential equation in terms of frequency, wavenumber and amplitude - that is a dispersion equation. Besides the frequency dispersion an amplitude dispersion occurs too. The distortion of the waveform depends on whether the Dispersion equation is elliptic or hyperbolic. The nonlinearity may produce phase jumps and discontinuities of the wavenumber. Author
- Numerical Mathematics